In recent years, in the process control system, there have been frequently used model predictive control technologies to construct a linear discrete time model on the basis of an impulse response or a step response of the process in order to conduct optimal control/operation while satisfying a large number of limits imposed on the process (plant) to calculate in sequence, from a predictive equation or formula derived from this model, such an optimal manipulated variables to minimize an cost function in quadratic form relating to deviations from reference or objective values of controlled variable's future values and manipulated variable's future values.
These technologies aim at determining manipulated variables applied at the present time point in order that a controlled variable future value to follow a reference value trajectory as close as possible is provided under a necessary minimum change in the manipulated variable.
Such model predictive control apparatus has merits as recited below.
1) Control response stable with respect to a process having a long dead time can be realized, PA1 2) Quick response property can be improved by a feed-forward control using a future reference value, PA1 3) Such model predictive control apparatus can be applied to a multi-variable control system as well, PA1 4) Without necessity of an accurate dynamic characteristic model of a controlled system, it is possible to easily design a control system from a step response, for example. PA1 5) By including a physical law or a non-linear dynamics of a controlled system (process) into the predictive model, fine control can be expected, PA1 6) It is possible to directly insert limit condition relating to an operation of a controlled system (e.g., upper and lower limiters, change rate limiters, etc.) into control rule, and the like. PA1 (1) Nishitani: Application of Model Predictive Control, Measurement and Control (Japanese) Vol. 28, No. 11, pp. 996-1004 (1989), and PA1 (2) D. W. Clarke & C. Mohtadi: Properties of Generalized Predictive Control, Automatica 25-6 pp. 859 (1989), etc. Particularly, in the literature (2), a Generalized Predictive Control (GPC) including various model predictive control systems has been proposed. In accordance with this control system, when a future reference value y* is given, a control response future value y(k+i)(i=1, . . . , Np) is predicted on the basis of a model of a controlled system (process) to calculate or determine a manipulated variable increment .DELTA.u(K) which minimizes a control cost function indicating control performance: ##EQU1## where parameter L is a prediction starting time, parameter Np is a prediction horizon, parameter Nu is a control horizon, parameter .lambda. is a weighting factor or coefficient, and D(Z.sup.-1) is a pole assignment polynomial. PA1 (3) Ohya and Iino "Model predictive control system in which constrains relating to controlled variable and manipulated variable are taken into consideration" (Preliminary Report of Science Lecture Meeting No. 29 of Measurement Automatic Control Society JS-2-4, p. 19, July (1990)), PA1 (4) Ohya and Iino "Model Predictive Control System" (Japanese Patent Application No. 111800/1990), and PA1 (5) Iino and Ohya "Model Predictive Control Apparatus" (Japanese Patent Application No. 138541/1990), etc.
Until now, various predictive control systems have been proposed. These systems are explained, e.g., in the following literatures.
In this control technology, since a predictive equation for determining future values of controlled variables or manipulated variables is represented by a function relating to past controlled variables or manipulated variables, prediction is carried out every time on the basis of past controlled variables or manipulated variables so that a controlled variable's future value becomes closer to a corresponding reference or objective value to determine a manipulated value applied at that time point. At this time, it is necessary to determine manipulated variables in order to satisfy the limit conditions relating to controlled variables/manipulated variables.
Meanwhile, as a general method of determining an optimal solution to minimize an cost function in a quadratic form while satisfying the limit conditions or constraints, there is a quadratic programming (QP) (With respect to QP, see Konno and Yamashita "Non-linear Programming" (Nikka Giren), Sekine "Mathematical Programming" (Iwanani Shoten), etc.). In order to use this QP, the cost function and the constraints must relate to only manipulated variables which are a parameter to be optimized.
However, as the constraints imposed on the process, there are not only those relating the manipulated variable which is a parameter to be optimized, but also those relating to controlled variable or those relating to controlled variable change rate. Accordingly, with conventional control systems, it was impossible to solve manipulated variables which can satisfy the above-mentioned latter constrains by QP as well.
As stated above, in the conventional model predictive control technology, since while there exist not only constrains imposed on the process relating to manipulated variable but also those relating to controlled variable and controlled variable change rate, manipulated variables which satisfy constrains relating to those controlled variables could not be solved by QP, it was impossible to conduct a control in which constrains relating to controlled variable with respect to the process are also taken into consideration.
It is to be noted that several of model predictive control systems in which constrains relating to controlled variable/manipulated variable/future value thereof of the process are taken into consideration have been already proposed by the inventors of this application. For example, there are
In accordance with these control systems, upper and lower limit conditions expressed below with respect to values from a present or current time k up to a certain time point in future are given to a controlled variable y(k), a controlled variable change rate .DELTA.y(k)=y(k)-y(k-1), a manipulated variable u(k), a manipulated variable change rate .DELTA.u(k)=u(k)-u(k-1): EQU y.sub.min (k+i).ltoreq.y(k+i).ltoreq.y.sub.max (k+i) (2) EQU .DELTA.y.sub.min (k+i).ltoreq..DELTA.y(k+i).ltoreq..DELTA.y.sub.max (k+i)(3)
where i=1, 2, 3, . . . Np (Np is a prediction horizon and indicates a time range in which a controlled variable predictive value is taken into consideration). EQU u.sub.min (k+i).ltoreq.u(k+i).ltoreq.u.sub.max (k+i) (4) EQU .DELTA.u.sub.min (k+i).ltoreq..DELTA.u(k+i).ltoreq..DELTA.u.sub.max (k+i)(5)
where i=0, 1, 2, 3, . . . Nu (Nu is a control horizon and indicates a time range of a future optimal manipulated variable calculated at a time by control operation). Then, manipulated variables to minimize the above-mentioned cost function J in a quadratic form are calculated while satisfying the above-mentioned upper and lower limit conditions to give the manipulated values thus calculated to a controlled system.
Meanwhile, in order to execute the above-described model predictive control, it is necessary to select in advance equations of the predictive model, and a large number of various control parameters included in the control cost function (1) or the upper and lower limit equations (2) to (5). Further, a process operator must suitably change the predictive model equation and/or various control parameters with a view to rationally adjusting diverse future reference value response characteristics or a large number of limit conditions depending on the operating condition varying every moment on the basis of the operation experience of the operator.
Accordingly, in the model predictive control, it is necessary to monitor and adjust parameters more than those in the conventional PID control. In addition, it is necessary to manipulate a plant operation so that various operation indices such as economical cost function, etc. indicating the operation cost, or the production amount of the process, etc. are satisfied while making a comparison between a present process state and a future process state.
However, a console which has been used for a conventional PID control has only a function to indicate or display a present operating state, or present and past operating states. Accordingly, simply using such a console for a model predictive control makes it difficult to conduct an accurate display of information and quick inputting operation.
The conventional model predictive control system is of a structure such that a model predictive control operation unit and control parameters calculation means are provided with respect to one input/output process. Namely, a process of one input/output system having a single manipulated variable and a single controlled variable is an object to be controlled.
However, many processes such as chemical, iron and steel, cement, paper making, foods or the like constitute a multivariable system (multi-input/output system) where a plurality of control variables such as temperature, pressure, flow rate, liquid level, and the like interfere with each other. Accordingly, an effective control system is expected for these controlled systems. In the case where the model predictive control is applied to these controlled systems, the following problems arise.
First, in these multi-input/output systems, there are instances where the number of manipulated variables and the number of controlled variables are different. In a multi-variable control system design method using an easily available transfer function conventionally proposed, it is the premise that the number of manipulated variables and the number of controlled variables are equal to each other. For example, an example thereof is described in "Design Theory of Linear Control System" (Japanese) Publication of Society of Instrumentation, Control Engineers, Chapter 6 (pp. 186-221). Accordingly, this design method cannot be used for design of the model predictive control system as it is.
Hence, a model predictive control system which can be applied also in the case where the number of manipulated variables and the number of controlled variables are different is required.
Secondly, in the model predictive control system, since the characteristic of the control system, particularly stability or robust property with respect to characteristic change, i.e., stability margin in so called a Nyquist stability criterion varies to much degree depending on how to select cost function parameters L, Np, Nu, .lambda., D(Z.sup.-1) included in the above-described cost function of the equation (1), it is necessary to suitably make adjustment (tuning) of the above-mentioned parameters at the time of starting of a control apparatus.
However, in the conventional model predictive control apparatus, the relationship between the cost function parameters and the control characteristic is not caused to become clear, so an operator empirically determined these cost function parameters while repeating trial-and-error. For this reason, labor is required for making an adjustment so that the control system is sufficiently stabilized, and it takes much time for starting of the control apparatus.
Further, in the conventional model predictive control systems, since control operation is carried out by placing emphasis on minimization of the cost function of the equation (1), there may take place the case where a closed loop pole determining a transient response characteristic of the control system cannot be suitably assigned. As a result, there may take place the problem that even if the control response is stable or quick, there results an oscillatory response form.
An object of this invention is to provide a model predictive control apparatus directed for a controlled system of multi-input/output including the case where the number of manipulated variables and that of controlled variables are different, and capable of calculating, by using QP, optimal manipulated variables to minimize an cost function while satisfying not only the limit condition relating to manipulated variables, but also the limit condition relating to controlled variables and their change rates.
Another object of this invention is to provide an input device suitable for a control apparatus of the model predictive control system.
A further object of this invention is to provide a model predictive control apparatus such that cost function parameters are automatically set to respective optimal values.
A still further object of this invention is to provide a model predictive apparatus in which an oscillation of a controlled value y in a rise response characteristic is suppressed.